Brasenose College is currently inviting applications for the prestigious Nicholas Kurti Senior and Junior Research Fellowship in the Sciences. These are non-stipendiary Fellowships which come with Senior Common Room membership (including free meals in college) and research and hospitality allowances.
Our new short film series 'Show Me the Maths' doesn't beat about the mathematical bush. It gets right down to it. Down, that is, to the maths, in all its crucial, complex, sometimes incomprehensible (even to other mathematicians) guises. It's what mathematicians do.
The series will feature research in Number Theory, Mathematical Biology and the History of Mathematics, amongst others. First up: Arun Soor.
11:00
Level lines of the massive planar Gaussian free field
Abstract
The massive planar Gaussian free field (GFF) is a random distribution defined on a subset of the complex plane. As a random distribution, this field a priori does not have well-defined level lines. In this talk, we give a meaning to this concept by constructing a coupling between a massive GFF and a random collection of loops, called massive CLE_4, in which the loops can naturally be interpreted as the level lines of the field. This coupling is constructed by appropriately reweighting the law of the standard GFF-CLE_4 coupling and this construction can be seen as a conditional version of the path-integral formulation of the massive GFF. We then relate massive CLE_4 to a massive version of the Brownian loop soup. This provides a more direct construction of massive CLE_4 and proves a conjecture of Camia.
Oxford Sparks are looking for someone to explain why all of the small bits of washing end up inside your duvet?
This major issue is in the news because one of their videos was taken up by Radio Oxford and the DJ sprung the duvet question on them during the live interview.
So they are looking for someone to give an answer to the question, ideally a mathematical answer, in video form.
If you are interested, contact Dyrol. They will make the video with you.
On the $(k+2,k)$-problem of Brown, Erdős and Sós
Abstract
Brown-Erdős-Sós initiated the study of the maximum number of edges in an $n$-vertex $r$-graph such that no $k$ edges span at most $s$ vertices. If $s=rk-2k+2$ then this function is quadratic in $n$ and its asymptotic was previously known for $k=2,3,4$. I will present joint work with Stefan Glock, Jaehoon Kim, Lyuben Lichev and Shumin Sun where we resolve the cases $k=5,6,7$.
During the pandemic, you may have seen graphs of data plotted on strange-looking (logarithmic) scales. Oliver will explain some of the basics and history of logarithms, and show why they are a natural tool to represent numbers ranging from COVID data to Instagram followers. In fact, we’ll see how logarithms can even help us understand information itself in a mathematical way.
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